This project addresses a variety of problems related to protein structure and folding, and uses methods of modern statistical mechanics. Current work focuses on two problems. The first problem is developing an objective measure of accuracy for protein structures determined by multi-dimensional NMR. A successful solution of this problem would yield a measure of accuracy analogous to the R factor in x-ray structure determination. The second problem is the determination of the accuracy requirements for potential functions to yield reliable predictions of protein structure. Solution of this problem would give molecular modelers realistic targets for their work and would provide a measure of confidence for a given model. An essential part of both of these problems involves the development and exploration of new techniques for incorporating distance constraints into the theory of protein structure. In the past year we have carried out extensive computer simulations of proteins with distance constraints. These simulations used a theoretical approach that we developed earlier. Without this method these simulations could not be done, even with the very simple protein models that we used. We are extending this theoretical approach to take into account the stiffness of the protein backbone in a more rigorous manner by using stiff (also known as semi-flexible or "worm-like") polymer models in our calculations. In the past year we have verified that a standard technique in statistical mechanics, mean field theory, can be used to calculate important conformational properties of stiff polymers with high accuracy. We plan to apply this technique to stiff polymers with distance constraints and compare the results to recent experiments. We shall also collaborate with Dr. Robert L. Jernigan of the NCI on further applications of these approaches to proteins. We are continuing our efforts to understand the physical chemistry of protein folding. In the past year we have worked on a theory of the nucleation of native structure in protein folding. This work combines the results of a detailed analysis of experimental data with sophisticated ideas in statistical mechanics. We are starting a collaboration with Dr. William A. Eaton of the NIDDK on the kinetics of protein secondary structure formation.